Any mathematicians here?
Hello! I'm a mathematician and I've been using ChatGPT 6 Astra as my main assistive tool for my Master's thesis. I've started using ChatGPT (been using ChatGPT ever since 5.5 came out) when it started to become really good at generating proofs. However, one of the main issues of AI-generated proofs is that they are sometimes unnecessarily wordy and "robot-like" (which is expected). As the mathematician, I have to unpack these proofs myself and improve it so they are understandable and readable to humans. Sometimes, the proofs are too difficult to understand that I have to prove them myself with a more granular assistance from ChatGPT which takes some time. However, it does seem possible for these AI generated proofs to be readable and humanized with the appropriate prompts the first time, with minimal need to manually "humanize" the proofs. Does anyone know how to do this? Is there a specific prompt that allows for proofs to be non-"machine" like? My current prompt goes something like: " Give me a rigorous, complete, detailed, concise, formal mathematical proof to the following proposition.:[insert some unproved proposition here]. Make sure to be direct, and straightforward. Take time think about the structure of your proof. Avoid "Step 1", "Step 2," that is, avoid compartmentalizing your proof. However, be clear with what needs to be shown next (WTS or Want To Show) which should be inside "( WTS )" to indicate that its not actually part of the proof but to guide the reader. Do not redefine variables too much if not absolutely needed." Is this good? (I mean probably not because I always get hard-to-understand proofs) If not, how can I improve it? I know I cannot simply task the clanker to "humanize " the generated proof. I want to know how to do it systematically rather than simply sounding like a human (not via "Act like a human" or "Sound like a human" or something ridiculous huahua) Thank you for anyone who can answer.